>>1111683295lbs (133kg) here, down from 360 (163) back in March. I only bought the bike when I got down to 310 or so, and did a bunch of research beforehand and got a frame rated for 300lbs. Haven't had a flat yet but I'm sure it's coming unless I keep the pressure on myself.
Like people are saying keep your tire pressure up, check it literally every time you ride and top it off to an appropriate level before you get on it. My hybrid's tires can lose up to 10 PSI overnight since they're so damn skinny.
Also, don't make riding a bike the only thing you're doing for exercise. Unless you're going uphill a lot it doesn't actually burn all that much energy since it's a very efficient method of travel. You'd be surprised with the results walking can get you. Also, figuring out a simple dumbbell workout you can do at home is another great way to burn calories and improve your conditioning, flexibility, and overall strength.
Diet is just as fucking important, by the way. It doesn't help to burn 4000 calories in a day if you eat 4500. If you don't know how many you're burning and consuming, get on that shit. Consult a nutritionist if you can afford it, otherwise there's a shit-ton of apps and websites out there that will provide you with loose guidelines to figure out what your intake and daily burn levels are. Quit drinking sodas and juice and sweetened ice tea and lemonade and beer and whatnot. Stick to water 99% of the time. Don't be afraid to cheat once in a while for the sake of your psychological endurance, but make sure it's just once in a while (special occasions maybe) and if you're going to cheat make it fucking count. Don't waste a cheat day on some prepackaged garbage from the convenience store. Have a fucking steak and savor every bite. Something like that.
Most of all, keep shit gradual. If you try to do a bunch of weight loss all at once you will crash in some way, either physically or mentally, and from there it's all to easy to backslide.